Estimation of Fingertip Force from Surface EMG

A Multivariate Bayesian Mixture of Experts Approach

Tara Baldacchino

, William Jacobs

, Sean R. Anderson

, Keith Worden

and Jennifer Rowson

Dynamics Research Group, Department of Mechanical Engineering, University of Shefﬁeld, Shefﬁeld, U.K.

Department of Automatic Control and Systems Engineering, University of Shefﬁeld, Shefﬁeld, U.K.

Keywords:

sEMG Signals, Finger Force Regression, Variational Bayes, Multivariate Mixture of Experts, Prosthetic Hand.

Abstract:

Improving the dexterity of active prostheses is a major research area amalgamating machine learning algo-

rithms and biosignals. A recent research niche has emerged from this- providing proportional control to a

prosthetic hand by modelling the force applied at the ﬁngertips using surface electromyography (sEMG). The

publicly released NinaPro database contains sEMG recording for 6 degree-of-freedom force activations for

40 intact subjects. In this preliminary study the authors successfully perform multivariate force regression

using Bayesian mixture of experts (MoE). The accuracy of the model is compared to the benchmark set by

the authors of NinaPro; comparable performance is achieved, however in this work a lower dimensional fea-

ture extraction representation obtains the best modelling accuracies, hence reducing training time. Inherent

to the Bayesian framework is the inclusion of uncertainty in the model structure, providing a natural step

in obtaining conﬁdence bounds on the predictions. The MoE model used in this paper provides a powerful

method for modelling force regression with application to actively controlling prosthetic and robotic arms for

rehabilitation purposes, resulting in highly reﬁned movements.

1 INTRODUCTION

The rapidly developing state of the art in hand pros-

thetics is seeing the advancement of active prostheses

capable of highly dexterous kinematics with a high

degree-of-freedoms (DoF). The advent of this new

generation of prostheses provides a challenge for the

bio-robotics and rehabilitation engineering communi-

ties in developing sophisticated control strategies that

are capable of accurately predicting a large range of

human movements from user intent.

The feasibility of ﬁne movement detection of the

upper limb has progressed rapidly in recent years, par-

tially due to advances in machine learning techniques.

There has been a bridging of the machine learn-

ing and rehabilitation robotics communities, bring-

ing together state-of-the-art robots/prosthetics and ad-

vanced algorithms (Castellini and van der Smagt,

2009). A variety of techniques are available for

obtaining biosignals for use as a human-machine-

interface (HMI), (Lebedev and Nicolelis, 2006). Sur-

face electromyography (sEMG) has become increas-

ingly popular as an HMI because of distinct advan-

tages in providing a non-invasive, relatively simple

and low cost method for voluntary activation.

Harnessing sEMG signals for the control of hand

prosthetics has a long history (Saridis and Gootee,

1982). However, until recently the control of pros-

thetics via sEMG was largely restricted to on-off con-

trol, often achieved by the classiﬁcation of various

hand/wrist movements (Peleg et al., 2002). Most of

the literature concentrates on classifying these move-

ments using sEMG signals by applying appropri-

ate classiﬁer techniques, see (Ferguson and Dunlop,

2002; Farrell and Weir, 2008; Atzori et al., 2012)

among others. A more recent and exciting new area is

the domain of proportional control by performing re-

gression between sEMG and the force applied at the

ﬁngertips. This has the potential to provide the user

with a much greater functionality in multiple DoF

(Muceli and Farina, 2012).

Previous studies aimed at achieving proportional

control have met with some success. One of the

ﬁrst investigations into force regression was done by

(Castellini and van der Smagt, 2009) where feed-

forward neural networks and support vector machines

(SVM) were used for both classiﬁcation of move-

ments, then separately for force control at the ﬁnger-

tips. More recently ﬁnger force control has been per-

formed using; SVMs (Castellini and K

oiva, 2012) and

270

Baldacchino T., Jacobs W., Anderson S., Worden K. and Rowson J..

Estimation of Fingertip Force from Surface EMG - A Multivariate Bayesian Mixture of Experts Approach.

DOI: 10.5220/0005260402700276

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2015), pages 270-276

ISBN: 978-989-758-069-7

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

different nonlinear kernel functions trained via ridge

regression (Gijsberts et al., 2014). Linear and nonlin-

ear techniques were analysed in (Hahne et al., 2014)

for regression analysis of wrist movements, includ-

ing a mixture of experts (MoE) model limited to two

experts and trained using iterative reweighted least

squares separately for each DoF.

In this work the authors propose a novel frame-

work for performing force regression for ﬁnger con-

trol using a ﬂexible multivariate Bayesian MoE

model. To the authors’ knowledge, using both a

Bayesian approach and MoE models to identify ﬁn-

ger force regression from sEMG signals has not been

performed before. The adoption of a MoE model de-

scribes the natural sEMG/force relationship by break-

ing down different movements into individual linear

models. Furthermore, the neuromusculare and biome-

chanics of ﬁnger movements are typical of biolog-

ical systems in that they are subject to uncertainty,

which the authors desire to characterise as an intrin-

sic part of the modelling algorithm. Therefore the

approach proposed here is to perform the estimation

using Bayesian inference. The Bayesian framework

inherently incorporates uncertainty into the training

of the model via distributions over the parameters.

It also naturally allows the evaluation of conﬁdence

bounds of the predicted signal thus providing a per-

formance check of the model at hand.

The MoE model was introduced in (Jacobs et al.,

1991). It probabilistically divides the input space of

a system using gates and allows experts to specialise

on certain regions of the input space. A powerful fea-

ture of MoE models is that the gates allow soft splits

of the input space that are functions of some or all of

the input variables. There are various different struc-

tures of the MoE model, and numerous methods for

training the model, see (Yuksel et al., 2012), and ref-

erences therein, for a recent review. The MoE model

is trained using variational Bayesian expectation max-

imisation (VBEM) using analytical closed form equa-

tions providing fast training times. Also, this form of

MoE described is capable of modelling several out-

puts simultaneously at little additional cost compared

to training a single output MoE, and hence it is re-

ferred to as multivariate Bayesian MoE. The MoE

model structure and training framework used in this

paper follows the work in (Baldacchino et al., 2014b),

and further developed in (Baldacchino et al., 2014a).

The rest of the paper is structured as follows. Sec-

tion 2 describes the sEMG/force dataset used in this

paper, along with preprocessing methods for sEMG

signals. The multivariate Bayesian MoE framework

is given in Section 3, and results on the sEMG/force

dataset are presented in Section 4.

2 NinaPro DATA

This section gives a brief description of the data used

in this paper: the second version of the publicly re-

leased NinaPro (Non-invasive Adaptive Prosthetics)

database. Details of the preprocessing performed on

the data are also given.

2.1 The Dataset

The NinaPro database contains surface sEMG record-

ings collected from 40 intact subjects while perform-

ing a large number of common hand movements and

grasp positions, including measurement of the applied

forces at the ﬁngertips (Gijsberts et al., 2014).

The data analysed in this paper consists of sEMG

recordings collected while subjects produce a set of

nine force patterns given in Table 1, by pressing down

with one or more digits. Corresponding force mea-

surements were considered (6 signals): ﬂexion of the

ﬁve digits as well as abduction of the thumb. sEMG

signals were recorded by 12 electrodes on the arm.

The 12 electrodes consisted of: 8 equally spaced

around the forearm at the height of the radio-humeral

joint, one on the ﬁnger extensor and ﬂexor muscles

respectively, and one each on the biceps and triceps

(Figure 1). Each subject had to perform each of the

9 movements 6 times. In order to prevent muscle

fatigue, a rest period was enforced in between each

movement and each repetition. More information and

detail regarding the setup and data collection can be

found in (Atzori et al., 2012; Gijsberts et al., 2014).

Table 1: Description of the 9 force movements.

# Movement Description

F1-F4 Flexion of little through to index ﬁngers.

F5/F6 Abduction/Flexion of the thumb.

F7 Flexion of the index and little ﬁnger.

F8 Flexion of the ring and middle ﬁnger.

F9 Flexion of the index ﬁnger and the thumb.

2.2 Data Preprocessing

The data preprocessing employed in this paper fol-

lows the proposed control scheme found in (Gijsberts

et al., 2014). All the data was ﬁrst standardised to

be zero mean and unit variance using statistics calcu-

lated solely from the training set. The data was then

split into a training and testing set based on the repe-

tition of movements; the second and ﬁfth repetitions

were used for testing and the four remaining repeti-

tions were used for training.

The signals were segmented into windows and FE

was performed on the windowed data. The signals

EstimationofFingertipForcefromSurfaceEMG-AMultivariateBayesianMixtureofExpertsApproach

271

Figure 1: Placement of the 12 sEMG electrodes on the arm.

were segmented into windows of 400ms (800 sam-

ples) with a sliding window increment of 10ms (20

samples). Regression was then performed on the ex-

tracted features using the method described in Section

3. For computational feasibility the training set was

subsampled by a factor of 10 (at regular intervals) re-

sulting in approximately 3000 data points for training.

Three commonly used sEMG feature extractions

(FEs) are considered and compared in this work;

the root mean square (RMS), the marginal discrete

wavelet transform (mDWT) and sEMG histogram

(HIST). These FEs were chosen in order to compare

with the benchmark set in (Gijsberts et al., 2014),

and details can be found there. The RMS is a low

dimensional FE where the dimensionality of the fea-

ture space is the same as the number of inputs (in this

case 12), whilst the mDWT and HIST are high di-

mensional FEs having effective input dimensions of

36 and 240 respectively.

3 MULTIVARIATE BAYESIAN

MIXTURE OF EXPERTS

In Section 3.1 the multivariate MoE regression model,

including a probabilistic model, is deﬁned based on

the MoE model developed in (Baldacchino et al.,

2014a). Training of the MoE model within a Bayesian

framework is discussed in Section 3.2.

3.1 Multivariate MoE Regression

Model

A MoE model with M regression experts, at time in-

stant n, is given by

∑

i=1

, θ

) f

, W

) , (1)

where x

= [x

, . . . , x

] ∈ R

1×d

is the input vector,

and y

= [y

, . . . , y

] ∈ R

1×d

is the corresponding

output vector. The i

expert function is restricted to

be linear such that f

, W

) = W

1] (the 1 repre-

sents a bias term). W

∈ R

+1×d

is the matrix rep-

resenting the expert weights. The i

gating function,

(·), is a normalised Gaussian function.

Given that N training data points are available,

then X = [x

, . . . , x

] ∈ R

N×d

and Y = [y

, . . . , y

] ∈

N×d

. The joint complete-data likelihood is ex-

pressed as

p(X, Y, Z|π

π, Θ

Θ) =

∏

n=1

∏

i=1



N (x

|µ

, Λ

−1

)

× N (y

1], χ

−1

)



(2)

where N is the Gaussian distribution. Z =

}

M,N

i=1,n=1

∈ R

N×M

, are the latent variables such

that if (x

, y

) was generated from the i

expert

then z

= 1, else it is 0. The gate parameters are

[π

π, θ

] = [π

π, {µ

µ Λ

Λ}], where µ

µ = {µ

}

i=1

is the mean

and Λ

−1

= {Λ

−1

}

i=1

is the covariance matrix. π

π =

{π

}

i=1

are the mixing coefﬁcients satisfying π

≥ 0

and

∑

i=1

= 1. The expert parameters are θ

W , χ

χ], where W

W = {W

}

i=1

is the multidimensional

parameter weight matrix and χ

−1

= {χ

−1

}

i=1

is the

covariance matrix. The set of unknown model param-

eters is given by [π

π, Θ

Θ] = [π

π, θ

, θ

3.2 Variational Bayesian Learning

Conjugate priors are assigned to all the parameters ex-

cept for the mixing coefﬁcients π

π (which are treated as

non-random variables). The assignment of prior dis-

tributions follows that found in the literature (Ueda

and Ghahramani, 2002; Baldacchino et al., 2014a)

and appropriately adjusted for use with multivariate

output signals. The joint distribution of all the ran-

dom variables can be expressed hierarchically as,

p(Y, X , Z, Θ

Θ|π

π)

= p(Y, X|Z, π

π, Θ

Θ)p(Z|π

π)p(µ

µ, Λ

Λ)p(W

W , χ

χ|a

a)p(a

(3)

as shown in Figure 2.

An approximate Bayesian framework is used in

order to ﬁnd the posterior distribution of the param-

eters p(Θ

Θ, a

a|Y ), since the marginal likelihood P(Y )

consists of a complex integral. The choice of conju-

gate prior distributions, along with a latent variable

model is elegantly accommodated by the variational

Bayes expectation-maximisation (VBEM) framework

(Beal and Ghahramani, 2003). The VBEM algo-

rithm is an iterative process which updates approx-

imate posterior distributions for the latent variables

BIOSIGNALS2015-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

272

�

Figure 2: Graphical model for Bayesian multivariate

MoE model: the plate denotes N i.i.d observations (ob-

served=grey shading, unobserved=no shading), red cir-

cles=gate parameters, green circles=expert parameters,

square boxes=known hyperparameters and dashed circle in-

dicates a non-random parameter.

and model parameters sequentially. The approximate

posterior distributions are denoted by q(·) and re-

ferred to as variational posterior distributions.

The variational distributions of both the latent

variables and the parameters for the MoE model de-

scribed in this paper can be expressed in a factorised

form as follows,

q(Z, µ

µ, Λ

Λ, W

W , χ

χ, a

a) = q(Z)q(µ

µ, Λ

Λ)q(W

W , χ

χ)q(a

a) . (4)

Since conjugate priors for the model parameters were

used, the functional form of the variational distribu-

tions will be the same as the priors. The update equa-

tion for π

π is obtained using maximum likelihood tech-

niques. A posterior predictive distribution can also be

obtained such that predictions of the output to new

unseen inputs can be performed. This distribution is

expressed as p(y

, D), where D = [Y, X ] is the

training data, and n

= N + 1 is the new data point.

Details of the necessary equations can be found in

(Baldacchino et al., 2014a), and they are omitted here

for brevity (due to a lack of space).

4 RESULTS

Before implementing the training algorithm described

in the previous sections, the windowed data was stan-

dardised to zero mean and unit variance again. This

was done in order to simplify the assignment of hy-

perparameter values for the prior distributions which

were set in such a way so as to deﬁne broad priors.

4.1 Multivariate Bayesian MoE for

sEMG Data

The multivariate Bayesian MoE model is trained on

the data obtained from all 40 subjects, and all the

6 forces are trained together at negligible additional

cost compared to a single output. The algorithm is ini-

tialised with 10 experts since there are 9 movements

and a rest period. Preliminary results indicated that

the HIST FE is impractical in the context of this work

due to such a high dimensionality of the feature space.

Thus the algorithm was run for the mDWT and RMS

FEs, and a comparison between the two is considered.

The performance of the ﬁnal models is analysed using

a normalised root mean square error (NRMSE, which

is the RMSE divided by the range of the output), and

the coefﬁcient of determination (R

Figure 3 shows the average NRMSE across all

subjects (averaged over the 6 DoF force activations)

for the two FE representations (mDWT and RMS).

NRMSE (%)

Subjects

RMS

0 10 20 30 40

NRMSE (%)

Subjects

mDWT

0 10 20 30 40

Figure 3: A plot of average NRMSE for the model obtained

for each subject for the mDWT and RMS FEs. The red

dashed line represents the mean NRMSE (over the 40 sub-

jects), while the black dashed lines represent ± one std.

All subjects achieve an acceptable level of perfor-

mance, with Subject 35 for mDWT and Subject 36 for

RMS having the worst NRMSE of 8.07% and 8.11%

respectively. The best performance was achieved by

Subject 8 for mDWT and Subject 33 for RMS having

an NRMSE of 2.99% and 2.8% respectively. The val-

ues of the NRMSE are comparable to those reported

by (Castellini and van der Smagt, 2009) where the au-

thors analyse ﬁnger force regression using SVM for a

different dataset, and report an average NRMSE of

7.89%. The mean and unit standard deviation (std)

for both R

and NRMSE are reported in Table 2.

Both types of FE techniques achieve comparable

EstimationofFingertipForcefromSurfaceEMG-AMultivariateBayesianMixtureofExpertsApproach

273

Table 2: % average R

and NRMSE ± one std.

Feature type Average R

Average NRMSE

mDWT 88.21±5.30% 4.82±1.11%

RMS 89.81±5.00% 4.44±1.06%

performance, however it is interesting to note that the

RMS FE performs better than the mDWT. This is in

contrast to that reported in (Gijsberts et al., 2014),

where they obtain R

values of 91.74% and 88.93%

for mDWT and RMS respectively for a exp-χ

ker-

nel ridge regression. The RMS feature provides a

much simpler FE representation, which also results in

much faster training of the data (on average RMS took

5.47min compared to 13.3min for mDWT for 100

runs). The RMS FE is also quicker to compute, and

for this training data the preprocessing time took on

average 5.9s for RMS versus 417.5s for mDWT. RMS

FE also allows a natural interpretation between the in-

puts and outputs, because the inputs are the physical

sEMG signals themselves.

To investigate the performance of the models on

each of the 9 force patterns, the average NRMSE

per pattern is shown in Figure 4. Patterns involving

the individual activation of the four ﬁngers (F1-F4)

are all characterised by high performance, and ad-

duction/abduction of the thumb (F5) achieves com-

parable performance (but with a slightly higher vari-

ance). The rest of the four movements (F6-F9) have

a slightly worse performance, especially those move-

ments involving ﬂexion of the thumb (F6 and F9).

F1 F2 F3 F4 F5 F6 F7 F8 F9

Force Pattern

NRMSE (%)

mDWT

RMS

Figure 4: A plot of the average NRMSE for each force pat-

tern for mDWT and RMS FEs. The error bars indicate unit

std.

Several authors, for example (Castellini and

oiva, 2012), have attributed the fact that predictions

of thumb movements are worse than for other ﬁngers

due to no sEMG activity being recorded from the ma-

jority of the thumb muscles which are located at the

wrist. The RMS performs better than mDWT overall,

and again the values for the NRMSE are comparable

to those reported in the literature, such as (Castellini

and K

oiva, 2012). The R

values are not reported

for the individual force patterns since the condition

∑

−

) is not necessarily 0 and so the R

value can go negative even though the model provides

a good ﬁt. Thus, direct comparison to the benchmark

is not possible since it would result in an incorrect in-

terpretation. However, the NRMSE values reported

here highlight what the authors in (Gijsberts et al.,

2014) established: single ﬁnger movements are easier

to predict than multiple ﬁnger and thumb movements.

4.2 Predictions for RMS FE

The results reported in this section concern the mod-

els obtained when the RMS FE technique was used,

since it shows better performance than the mDWT

and it is computationally cheaper to work with RMS.

The top plot given in Figure 5 shows the predic-

tions (red) obtained on the testing data (blue) for the

fourth force DoF (index ﬂexion) for Subject 1. The

signals are plotted on a background of colours where

each colour indicates a particular expert. The 99%

conﬁdence intervals are also plotted (black dashed),

since these arise naturally from the Bayesian infer-

ence framework. The conﬁdence intervals comfort-

ably encloses most of the observed data (blue). In

both cases the model predictions of the force follow

the observed data well. Even more interesting is the

assignment of experts; the experts identiﬁed in the

training set are also the same ones used in the test

set. The rest period is almost always identiﬁed, and

it is assigned its own expert (bright green). Move-

ments corresponding to individual ﬁngers along with

ﬂex thumb, ﬂex index and little, and ﬂex index and

thumb are again assigned individual experts. Two ex-

perts are needed to model abduction of the thumb, and

this could be due to no sEMG activity being recorded

from the majority of the thumb muscles, and so this

presents difﬁculty in modelling it accurately. Flexion

of the ring and middle ﬁnger is modelled using the ex-

perts from both their corresponding individual ﬁnger

movements (dark green and pink). This assignment

of experts has the potential for further investigatory

work for classiﬁcation of ﬁnger movements.

The bottom plot of Figure 5 shows the predictions

for all 6 DoF force measurements of all the nine force

patterns. Again, all the forces and force patterns are

predicted accurately, and similar to (Gijsberts et al.,

2014) the model even learned the involuntary negative

forces which they attribute to synergistic or compen-

satory mechanisms.

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274

Number of Samples

Force (N)

Test Data

0 500 1000 1500 2000 2500

−5

−10

ex little ex ring ex middle ex index

abduct

thumb

ex

thumb

ex index

& little

ex ring

& middle

ex index

& thumb

Observed Data

Model Predictions

99% CI

Number of Samples

Force (N)

0 500 1000 1500 2000 2500

−5

−10

ex little ex ring ex middle ex index

abduct

thumb

ex

thumb

ex index

& little

ex ring

& middle

ex index

& thumb

Little Ring Middle Index Thumb Abduction Thumb Flexion

Figure 5: Top plot: Predictions (red) versus observed data (blue) including 99% conﬁdence intervals (dashed black) on the

test data of the fourth DoF force activation. The background of colours represent the individual experts. Bottom plot: A plot

of observed (solid) and predicted (dashed) forces for the second and ﬁfth repetitions of all nine force patterns. Each colour

corresponds to a force measurement. For both plots, black vertical lines indicates when a movement starts.

Integral to the Bayesian training is the use of au-

tomatic relevance determination (ARD), whereby non

inﬂuential inputs are ’turned off’ thus avoiding over-

ﬁtting and allowing the possibility of removing sur-

plus electrodes. The ARD values obtained from up-

dating the appropriate hyperparameters are analysed.

Figure 6 shows a box plot of the average ARD for

each sEMG input signal for all 40 subjects. Large

ARD values indicate that an input is heavily weighted

while low ARD values indicate that the particular in-

put is heavily attenuated. Not surprisingly, electrodes

11 and 12 (biceps and triceps) seem to have the least

effect on ﬁnger movement.

5 CONCLUSION

In this paper the authors propose a novel method for

the modelling of force regression from sEMG sig-

nals for the purpose of proportional control of pros-

thetic hands employing a multivariate Bayesian MoE

model. The algorithm presented provides fast learn-

ing of the data due to analytical closed form equa-

tions. The results on the 40 subjects are encourag-

ing since accurate predictions for several ﬁnger move-

ments are achieved. This method also highlighted that

better results can be achieved with a low dimensional

FE representation than with a higher one, thus reduc-

ing computational effort even further. The low dimen-

sional FE allows investigation into the inﬂuence of the

sEMG signals

ARD value

1 2 3 4 5 6 7 8 9 10 11 12

Figure 6: Box plot of average ARD values (over the number

of experts) for each sEMG input signal.

inputs on the force regression as the inputs are the

physical sEMG signals themselves. The fast manner

in which predicted outputs are generated suggests that

this method will be easily transferable to an online

situation for instantaneous proportional control of a

prosthetic hand (for a single data point it takes on av-

erage 16.8µs to generate a predicted output value). It

has been well documented within the literature that

for a method to be successful within a clinical ap-

plication, it should require minimum user training,

have low computational complexity and perform ad-

equately with few electrodes. The method presented

EstimationofFingertipForcefromSurfaceEMG-AMultivariateBayesianMixtureofExpertsApproach

275

in this work achieves all the above criteria. It will

be interesting to apply this framework to sEMG/force

data collected from amputees. As future work, the

authors are investigating the possibility of a simulta-

neous regression-classiﬁcation framework for ﬁnger

force control.

ACKNOWLEDGEMENTS

Authors T. Baldacchino and W. Jacobs would respec-

tively like to thank the Leverhulme Trust (130986)

and EPSRC (EP/K503149/1) for ﬁnancial support.

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BIOSIGNALS2015-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

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